class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> sum(m, vector<int>(n, 0));
        
        sum[0][0] = grid[0][0];
        for (int i = 1; i < m; i++) {
            sum[i][0] = grid[i][0] + sum[i-1][0];
        }
        for (int j = 1; j < n; j++) {
            sum[0][j] = grid[0][j] + sum[0][j-1];
        }
        
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                sum[i][j] = min(sum[i-1][j], sum[i][j-1]) + grid[i][j];
            }
        }
        
        return sum[m-1][n-1];
    }
};
